Sectioned shell puzzles

ABSTRACT

A plurality of pieces constitute the normal edge dissection of a polyhedron shell. Selections of said pieces can be used to reconstruct the shell perfectly. Male and female keys along the edges of each piece interfit to form the edges and corners of the shell perfectly. Cubic and tetrahral shells are illustrated. Selected pieces can be used to construct variously shaped shells. The pieces may be provided with binding holes through which binding pins may be inserted to hold adjacent pieces together.

United States Patent [191 Freedman June 25, 1974 SECTIONED SHELL PUZZLES[76] Inventor: Gerald Allen Freedman, PO. Box

503 Federal Station, Worcester, Mass. 01601 [22] Filed: Dec. 29, 1972[21] Appl. No.: 319,475

[52] US. Cl 273/160, 46/24, 46/30 [51] Int. Cl. A63f 9/12 [58] Field ofSearch 273/157 R, 160; 46/24,

[56] References Cited UNITED STATES PATENTS 5/1970 Gable 273/160 12/1970Williams et al. 273/157 R FOREIGN PATENTS OR APPLICATIONS 573,378 GreatBritain 46/25 1,913,383 9/1970 Germany 46/30 Primary Examiner-Anton O.Oechsle [57] ABSTRACT A plurality of pieces constitute the normal edgedissection of a polyhedron shell. Selections of said pieces can be usedto reconstruct the shell perfectly. Male and female keys along the edgesof each piece interfit to form the edges and corners of the shellperfectly. Cubic and tetrahral shells are illustrated. Selected piecescan be used to construct variously shaped shells. The pieces may beprovided with binding holes through which binding pins may be insertedto hold adjacent pieces together.

9 Claims, 5 Drawing Figures PAlENIEnJuuzsmn SHEET 2 OF 2 SECTIONED SHELLPUZZLES SUMMARY OF THE INVENTION Geometric shells can be sectioned in alogical way into interlocking puzzle pieces. Many piece selections ofpuzzle sets are possible and only a few will reform the original shell,in certain ways, perfectly. Some shell puzzles, especially the cube, canalso constitute a construction block toy where derived puzzle pieces areused to build shells of larger size and different shape than that of theoriginal shell.

BRIEF DESCRIPTION OF Tl-IE DRAWINGS FIG. 1 is a perspective view of theassembled, normal'edge dissection of a regular cube shell.

FIG. 2 shows a perspective view of six interlocking, planar puzzlepieces derived from the cube shell dissec tion.

FIG. 3 shows a binding pin.

FIG. 4 is a perspective view of the assembled, normal-edge dissection ofa regular tetrahedron shell.

FIG. 5 shows an outline view of four interlocking, planar puzzle piecesderived from the tetrahedron shell dissection.

DESCRIPTION OF THE INVENTION Any geometric solid can be conceived of asa shell, completely enclosing a single or plural hollow interiors.Geometric shells can be sectioned in logical and arbitrary ways into twoor more pieces that can be regarded as constituting a puzzle. Thisinvention concerns the regular shells of polyhedron solids, whoseinterior is a single compartment, whose interior and exterior surfacesare similar in shape, whose thickness is uniform, and whose edges areall line segments; particular dissections thereof called the normal-edgeand the abnormal-edge shell dissection; and a certain, limited,definition of puzzle piece formation.

While any regular geometric shell having at least one edge has uniquenormal-edge dissection, most shells yield largely dull puzzle pieces.Other polyhedron shells, irregular, deformed, and plural compartment,and other dissections as the normal-corner dissection, the facedissection, the unit dissection, and arbitrary dissections have lesserfascination as puzzles or value as construction block toys. Thenormal-edge and the abnormal-edge dissection of the regular cube andtetrahedron shells are of great interest and are described in detail asexamples of this method of shell dissection used to determine this classof sectioned shell puzzles.

The normal-edge dissection involves the normal dissection of shells anda further sectioning of shell edge pieces whereby interlocking male andfemale keys can be provided to derive puzzle pieces. The normaldissection of any regular shell proceeds as follows: Any shell havingone or more comers and/or edges has an extension where every shellsurface, exterior and interior, is continued beyond corner and edgeboundaries to infinity, respective to functions of shape. For everypoint on the exterior surface of a shell and the exterior surfaceextension there is a unique line segment, normal to the shell surfaces,having a length equal to the uniform thickness of the shell, with endpoints on the exterior surface or surface extension and on the interiorsurface or extension. Those points of the actual material of the shellare either (A) common to one and only one normal line segment, (B)common to exactly two distinct normal line segments, (C) common to threeor more distinct normal line segments. That material of a shell whosepoints form a system of adjacency and meet above condition (A) arecalled face pieces of the shell; condition (B), are called edge pieces;condition (C), are called corner pieces. That material of a shell whosepoints are common to two or more distinct normal line segments is calledthe shell frame. Usually a regular shell having of its exterior surfaceX faces, Y edges, and Z corners will, by the normal dissection,determine X face pieces, Y edge pieces, and Z corner pieces. The frameof the shell can also be understood as the union of all edge and comerpieces, and will be disconnected only when the shell embodies acontinuous curve surface.

7 Further sectioning of the normal dissection of polyhedron shells intothe normal-edge dissection proceeds as follows: Every exterior edge of apolyhedron shell, being a line segment, can be sectioned into 3 equalsegments, determining 2 section locations on every distinct exterioredge of the shell. Determined section locations will be present to theedges of the shell edge pieces (through the normal dissection) only whenevery exterior shell edge is greater in length than 3 or more times theshell thickness. Final sectioning, after normal dissection, is by way offlat planes, normal to the shell edges at section locations, sectioningedge pieces only into 3 parts. Section locations for the edge piece partdissection can be otherwise determined or arbitrarily positioned,however comprising key symmetry. 1

The assembled normal-edge dissection of a regular cube shell is shown inFIG. I and that of a regular tetrahedron shell is shown in FIG. 4.. Anypiece or connected combination of pieces of the dissection can beregarded as a puzzle piece, connected combinations considered as formedintegrally. The Full set of puzzle pieces of the dissection wouldconsist of an infinite quantity of every unique combination possible.More highly defined puzzle piece sets would consist of finite quantitiesof variously limited combinations. One such outstanding limited set isdefined as follows: Those combinations of pieces, face, edge part, andcomer that (I) lie in the same plane, (2) include a face piece, (3) havefor every distinct edge of the face piece either the central edge piecepart adjacent thereto (male key) or the two edge piece parts adjacent tothe central edge piece part (female key), (4) intrinsically include acorner piece only at adjacent female keys, (5) extrinsically include acorner piece only at adjacent male and female keys, and (6) includeevery possible arrangement of corner pieces present and/or absent toevery possible piece of above l,2,3,4,& 5. Corner pieces can not bepresent at adjacent male keys, being disconnected to the face piece atthese locations.

FIG. 2 shows the pieces of the above definition, parts l,2,3,4, & 5derived from the cube shell normal-edge dissection, FIG. 1. The dottedlines indicate possible locations of corner pieces as of parts 4,5 ,& 6of the definition. Comer pieces may be present and/0r absent to piece Ain 6 different ways,.to piece B in 10 different ways, to piece C in 6different ways, to piece D in 7 different ways, to piece E in 3different ways, and to piece F in 1 way, determining 33 differentlyshaped pieces in all. Considering construction of a cube shell fromthese pieces, there are 48 selections of S(6,6) =462 possible selections(definition parts 1,2,3) that provide the necessary 12 male and 12female keys exactly. Of these 48 selections, 8 provide the properquantity of 8, intrinsically included, comer pieces (definition parts1,2,3,4), while the other 40 selections can be adjusted to 8 corners, inmany different ways, by adding or subtracting corners (definition parts5,6) to form the shell perfectly.

The puzzle pieces derived from the above set definition, parts 1,2,3, &4for the normal-edge dissection of a tetrahedron shell, FIG. 4, are shownin outline, FIG. 5. Extending the definition to parts 5 & 6, there wouldbe 17 pieces in all. From S(4,4) 35 selections of pieces, there are 5that provide the necessary 6 male and 6 female keys exactly, and onlyone that intrinsically includes the proper quantity of 4 comer piecesexactly, that selection being the four outlined pieces K,L,M, and N ofFIG. 5.

An important property of a well defined set of sectioned shell puzzlesis that the derived pieces be capable of building shells of differentsize and shape than that of the original dissection. The cube shellpieces are extremely apt in this respect and a large quantity of puzzlepieces can constitute a construction block toy. However many largerbuilt shells could readily collapse. To prevent collapse, the pieceshave binding holes, indicated on the pieces of FIG. 2 by the smallcircles, and can be secured together in the same and at intersectingplanes by tapered binding pins, FIG. 3. In addition to the defineddissection puzzle pieces, a construction block toy can also include avariety of other blocks such as face, edge, and comer pieces of thedissection, as well as posts, columns, partians, doors, stairs, etc..These additional pieces would also have binding holes and theircombination with a large set of puzzle pieces produces a block toyhaving extensive scope of design. Cube block pieces, buildable in manyimaginative ways, can also be combined in many strange and interestingoffset patterns.

The regular shells of the five regular polyhedron solids all yieldfascinating normal-edge dissection puzzles. Of these, the tetrahedron isthe simlest puzzle and the cube the most intriguing construction blocktoy. Every other polyhedron shell has a unique normal-edge dissectionand an interlocking planar puzzle piece set, but, for the most part, thederived pieces fit together in few ways and are unable to builddifferently shaped shells extensively.

In the foregoing definition of sectioned shell puzzles only 1 male or 1female key is provided to the edges of planar puzzle pieces. Shell edgepieces could also be sectioned into any number of parts, in manydifferent ways, to provide any number of keys, in any combination, tothe edges of shell face pieces. Special or offset keying can limit thenumber of ways proper piece selections can be combined perfectly, but,in general, multikeyed pieces have an unpleasing, unnecessarilycomplicated appearance.

Many various materials can be used to compose the pieces of puzzles andconstruction block toys. Pieces can be transparent, colored, or opaque.The puzzle container itself can be a piece or pieces of the puzzle.Pieces could also have designs or further sectioned parts, holes, orpatterns, not directly related to the normal-edge or the abnormal-edgepolyhedron shell dissection.

Having set forth disclosure of my invention, I claim:

1. A puzzle comprising a finite number of puzzle pieces of a normal edgedissection of a polyhedron shell, wherein selections of said pieces canbe fit together to form the original polyhedron shell perfectly, each ofsaid pieces being planar and comprising an entire face of saidpolyhedron shell, each piece at each edge thereof having either acentrally located male edge key with female edge keys on opposite sidesthereof or a centrally located female edge key with male edge keys onopposite sides thereof, and each piece further including at each comer amale or a female key, a said selection of said pieces being equal innumber to the number of faces of a given polyhedron to form the facesthereof, with the male and female edge keys of said selected piecestogether forming the given polyhedron edges perfectly, and with the maleand female comer keys of said selected pieces together forming thecorners of the given polyhedron perfectly.

2. The puzzle of claim 1 where the section locations of the edge piecepart dissection number two and are located at the interior end points of3 equal edge segments of every exterior shell edge; and where everyexterior'shell edge is greater in length than 3 times the uniform shellthickness.

3. The puzzle of claim 1 where the section locations of the edge piecepart dissection number two and are located anywhere on the exterioredges of shell edge pieces.

4. The puzzle of claim 1 where the section locations of the edge piecepart dissection are any number 2 or more and are located anywhere on theexterior edges of shell edge pieces; and where plural edge keys areprovided to each edge of each piece in a manner similar to thesingle-keyed pieces.

5. The puzzle of claim 1 where the exterior edges of said polyhedronshell all have the same length.

6. The puzzle of claim 5 where said polyhedron shell is a cube.

7. The puzzle of claim 5 where said polyhedron shell is a tetrahedron.

8. The puzzle of claim 1 where a finite number of said puzzle piecesprovides selections of said pieces that are able to build shells ofdifferent size and shape than that of the original dissection andconstitute a construction block toy. 7 v 7 r 9. The construction blocktoy of claim 8 where said pieces have binding holes sectioned thereinand there are binding pins capable of engaging the binding holes

1. A puzzle comprising a finite number of puzzle pieces of a normal edgedissection of a polyhedron shell, wherein selections of said pieces canbe fit together to form the original polyhedron shell perfectly, each ofsaid pieces being planar and comprising an entire face of saidpolyhedron shell, each piece at each edge thereof having either acentrally located male edge key with female edge keys on opposite sidesthereof or a centrally located female edge key with male edge keys onopposite sides thereof, and each piece further including at each cornera male or a female key, a said selection of said pieces being equal innumber to the number of faces of a given polyhedron to form the facesthereof, with the male and female edge keys of said selected piecestogether forming the given polyhedron edges perfectly, and with the maleand female corner keys of said selected pieces together forming thecorners of the given polyhedron perfectly.
 2. The puzzle of claim 1where the section locations of the edge piece part dissection number twoand are located at the interior end points of 3 equal edge segments ofevery exterior shell edge; and where every exterior shell edge isgreater in length than 3 times the uniform shell thickness.
 3. Thepuzzle of claim 1 where the section locations of the edge piece partdissection number two and are located anywhere on the exterior edges ofshell edge pieces.
 4. The puzzle of claim 1 where the section locationsof the edge piece part dissection are any number 2 or more and arelocated anywhere on the exterior edges of shell edge pieces; and whereplural edge keys are provided to each edge of each piece in a mannersimilar to the single-keyed pieces.
 5. The puzzle of claim 1 where theexterior edges of said polyhedron shell all have the same length.
 6. Thepuzzle of claim 5 where said polyhedron shell is a cube.
 7. The puzzleof claim 5 where said polyhedron shell is a tetrahedron.
 8. The puzzleof claim 1 where a finite number of said puzzle pieces providesselections of said pieces that are able to build shells of differentsize and shape than that of the original dissection and constitute aconstruction block toy.
 9. The construction block toy of claim 8 wheresaid pieces have binding holes sectioned therein and there are bindingpins capable of engaging the binding holes to secure pieces together inthe same and at intersecting planes.